Preheat oven to 190 degrees C. Grease and dust with sugar 6 ramekins. Mix coconut and half the apricots together and divide between the ramekins. Drizzle each with 1 tablespoon golden syrup.
Mix butter and sugar with an electric mixer until pale. Beat in the eggs one at a time, then the coconut milk. Fold in the sifted flour and remaining apricots. Divide the pudding mixture between the ramekins.
Place the ramekins in a baking dish half-filled with warm water. Cover with foil and bake 40 minutes, then turn out the puddings while still hot.